@BalarkaSen in a question in simmons its given that let d be a real function on the nonempty set X which satisfies the three conditions that are
$d(x,y)>0$ and equal to 0 when x=y.
$d(x,y)=d(y,x)
d(x,y)<d(x,z)+d(z,y)and also equal to.
then it is called a pseudo metric but arent these conditions same as we have in a metric